Optimization Of Substrate Feed Flow Rate Biology Essay

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Fed-Batch Yeast Fermentation Process. Abstract-This paper presents Q-Learning (QL) algorithm based on optimization method to determine optimal glucose feed flow rate profile for the yeast fermentation process. The optimal profile is able to maximize the yeast concentration at the end of the process, meanwhile to minimize the formation of ethanol during the process. The proposed approach is tested under four case studies, which are different in initial yeast and glucose concentration. The results show that the proposed approach is able to control the process in a satisfactory way.

Keywords-Fed-Batch; Yeast Fermentation; Q-Learning

Introduction

During the past few decades, optimization has become the key issue in biotechnology industry in order to reduce the production cost. The strategy of optimization is to increase the product yields, meanwhile to ensure the product quality [1, 2, 3].

Normally, most of the strategies in yeast fermentation are controlling the nutrient (glucose) supply in order to obtain optimal performances. When the glucose feed rate is increased, it may form ethanol as an undesired by-product. The formation of ethanol deteriorates the quantity and quality of yeast at the end of the process. However, a decrease in glucose feed rate leads to a diminution in yeast growth rate [1].

In general, there are three basic operation modes used in industrial fermentation processes: continuous, batch, and fed-batch. For the continuous operation mode, substrate is added and products are removed continuously in the same rate. This can cause outflow of substrate, hence more substrate is needed. For the batch operation mode, substrate is added in the beginning stage, and then the final products are removed at the end of the process. This operation may increase the undesired by-product during the fermentation. The fed-batch operation mode is the most economic way among the three basic operations. The substrate feeding rate is varied during the process and the final products are removed from the fermenter. In this way, the provision of substrate as well as the formation of by-products can be controlled.

The common strategy used in industries to control this process is PI controller. The PI gains are usually tuned by human operators based on their experience. As a result, the operation is not always uniform and optimal productivity is seldom obtained [1]. In order to overcome this problem, various artificial intelligence (AI) approaches are proposed to control the process. The most famous used AI approaches in this process are fuzzy logic and neural networks [3, 4, 5]. However, both methods require either preset settings and data or deep understanding of the process.

The aim of this paper is to optimize the glucose feed flow rate for the yeast fermentation process using reinforcement learning (RL). The optimal glucose feed flow rate can be used to maximize the production of yeast at the end of the process, meanwhile to minimize the formation of ethanol during the process.

Reinforcement Learning

RL is an unsupervised machine learning algorithm that seeks to maximize a numerical reward signal [6]. Instead of utilizing examples of correct action, as in supervised learning methods, RL negotiates the problem of how an agent can learn a behavior through trial and error interactions with environment [7]. RL reinforces any evaluates to choose an action and a policy by reward/penalty [8]. Fig. 1 shows the framework of RL

Environment

Sensitive Unit

Learning Unit

Choice Unit

Reward/Penalty

Framework of RL [8]

In 1989, Watkins introduced a method of RL called Q-learning (QL) [9]. QL is a RL algorithm that attempts to learn a state-action pair value Q(s, a), whose value is the maximum discounted reward that can be achieved by starting in state s, taking an action a, and following the optimal policy thereafter [10]. Equation (1) describes the QL approach.

(1)

α and γ represent the learning rate and discount factor respectively. Both of them are positive scalar between 0 and 1 while Rt is the reward/penalty that the agent gained after executed an action a in state s.

However, the central issue in RL is defining the system states. RL has been successfully used by most of the researches for simple problems characterized by discrete state and action spaces. It is rare to use RL in process control because of the state and action spaces for the process control are continuum [11].

In order to overcome the state definition issue, divide-and-conquer method is introduced in this paper. The total fermentation time is divided into few sub-sections. Each of the sub-sections has a common time interval size. The aim of the QL for each sub-section is to obtain the optimal performance. All the glucose feed flow rates determined in each sub-section are combined together at the end of the process. This solution is called optimal glucose feed flow rate profile for the respective case.

The reward/penalty is calculated using optimization equation, as shown in (2) to (5).

(2)

(3)

(4)

(5)

where β1, β2, β3 = weight factors

ti = time for ith iteration

Fermentation Model Development

The model of an industrial fed-batch yeast fermentation process is divided into two parts: cell (kinetic) model and reactor (dynamic) model. The modeling equations are taken from [1].

Kinetic Model

The kinetic model of yeast metabolism assumes a limited oxygen capacity of yeast, leading to formation of ethanol under conditions of oxygen limitation and/or an excessive glucose concentration [1]. The kinetic model is expended as (6) to (16).

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

Dynamic Model

The dynamic model is based on mass balance equations described by glucose, ethanol, dissolved oxygen and yeast concentrations [1], as shown from (17) to (21). The model was constructed by completing the kinetics with substrate limitation and product inhibition [1].

(17)

(18)

(19)

(20)

(21)

The model parameters, as shown in Table I, are taken from [1, 4, 12]. Then, the proposed approach is tested under four cases with different initial yeast and glucose concentration, as shown in Table II. For Case I, initial yeast and glucose concentration are considered as appropriate. For Case II, initial yeast concentration is considered as appropriate and initial glucose concentration is considered as low. For Case III, initial yeast concentration is considered as low and initial glucose concentration is considered as appropriate. For Case IV, initial yeast and glucose concentration are considered as low.

Numeric values of the parameters in the fed-batch yeast fermentation model [1, 4, 12]

Parameters

Units

Value

0.1

3.5

0.612

0.585

0.05

0.3857

1.1236

0.4859

0.7187

0.5744

0.462

0.645

0.8896

0.238

0.255

2.943

0.03

0.21

325

2

0.006

700

16

0

4100

100

V(0)

50

325

The range of the glucose feed flow rate, F is varied from 0 to 4100 . The sampling time is chosen as 3.6 seconds or equivalent to 0.001 hour. The total fermentation time is selected to be 16 hours. The volume of fermenter is 100 m3. The cultural volume at the beginning, V(0) is set as 50 m3, and it must not exceed the volume of fermenter at the end of the process.

Initial concentration of yeast and glucose for five different cases

Case

Initial Yeast Concentration

Initial Glucose Concentration

I

8.0 (appropriate)

3.0 (appropriate)

II

8.0 (appropriate)

0.2 (low)

III

0.5 (low)

3.0 (appropriate)

IV

0.5 (low)

0.2 (low)

The proposed approach was programmed in MATLAB V7.9 and then the simulation was run on an Intel (R) Pentium (R) M processor based 2GHz with 512MB RAM.

Performances Of Non-Optimal Process

The simulation was run under all the initial conditions, as discussed in Section III, for a profile of the glucose feed flow rate as shown in (22).

(22)

Fig. 2 shows the profile of non-optimal glucose feed flow rate and culture volume for all cases. The performances of the fermentation model are shown in Fig. 3 and Fig. 4.

Non-optimal glucose feed flow rate profile (dashed line) and culture volume profile (solid line) for all cases

It can be observed from Fig. 3 that the performance of the non-optimal glucose feed flow rate profile is acceptable for Case I and Case II. However, the same feed flow rate profile is not suitable for the other two cases.

For Case I, it produces a higher yeast concentration at the end of the process compared to the Case II due to the higher initial yeast concentration. On the other hand, the reason of the total ethanol formation in Case III is higher than Case IV is because of Case III has a higher initial glucose concentration.

All the performances show that the final yeast concentration at the end of the process and the total ethanol formation during the process depends on the initial yeast and glucose concentration. A higher initial glucose concentration will produce more ethanol and vice-versa, whereas a higher initial yeast concentration will end up with a higher yeast concentration at the end of the process.

From Fig. 4, it can be seen that ethanol started to form when the specific growth rate exceeds the critical growth rate. For example, the specific growth rate for Case II exceeds the critical growth rate during the period from 0.5 hour until 1.0 hour. It increased production of ethanol during the same period, as shown in Fig. 3. Hence, in order to achieve the fermentation objective, it is important to ensure that the average specific growth rate is optimized near to the critical growth rate, as shown in (4).

Performances Of QL Algorithm

In order to improve the poor performances shown in Section IV, QL algorithm is proposed to determine the optimal glucose feed flow rate profiles for all cases. These optimal profiles are able to maximize the yeast production at the end of the fermentation, whereas to minimize the formation of ethanol during the fermentation. Fig. 5 shows

Note:

Yeast concentration (solid line)

Ethanol concentration (dotted line)

Glucose concentration (dashed line)

Dissolved oxygen concentration (dash-dot line)

Performances of non-optimal glucose feed flow rate profile for all cases

the optimal glucose feed flow rate profiles determined by QL for all cases. The performances of these optimal profiles for all the respective cases are shown in Fig. 6 and Fig. 7.

From the comparison between the performances shown in Fig. 3 and Fig. 6, Fig. 6 shows that the optimization performance for each case can be obtained using the respective optimal glucose feed flow rate profile determined by QL. It can be noted that the yeast concentration at the end of the process shown in Fig. 6 is much higher than shown in

Specific growth rate (dashed line) and critical growth rate (solid line) performances for all cases under non-optimal glucose feed flow rate profile

Fig. 3. In contrast, the formation of ethanol shown in Fig. 6 is much lesser than shown in Fig. 3.

Besides, QL is able to maintain the average specific growth rate near the critical growth rate, as shown in Fig. 7, compared to the Fig. 4. In general, the total computing time of QL varies between 50 seconds and 160 seconds. These results reveal that the proposed algorithm may be used in practical for optimization applications.

The effort of the proposed approach in order to maximize the yeast yield at the end of the fermentation, meanwhile to minimize the total ethanol formation during the fermentation is satisfactory. In future, the effectiveness of QL will be stressed by including disturbance effects.

Optimal glucose feed flow rate profiles (dashed line) determined by QL algorithm, and culture volume profiles (solid line) for all cases

Conclusion

The aim of this paper is achieved. QL seems to be a promising technique to obtain an optimal performance where limited knowledge is available on the particular process. The slow computing time curse of traditional QL can be eliminated by introducing divide-and-conquer method into it. In this project, the total computing time of the proposed approach varies between 50 seconds and 160 seconds. With the fast computing time of the proposed approach, it can be used in practical. From the simulation results, the final yeast

Note:

Yeast concentration (solid line)

Ethanol concentration (dotted line)

Glucose concentration (dashed line)

Dissolved oxygen concentration (dash-dot line)

Performances of optimal glucose feed flow rate profiles for all the respective cases

concentration at the end of the process and the total ethanol formation during the process depend on the initial yeast and glucose concentration respectively. A higher initial yeast concentration generally causes lesser formation of ethanol during the process. However, a higher initial glucose concentration will cause higher ethanol concentration due to the excessive glucose concentration inside the fermenter. In future, the effectiveness of QL will be stressed with few disturbance effects.

Specific growth rate (dashed line) and critical growth rate (solid line) performances for all cases under the respective optimal glucose feed flow rate profile

Nomenclature

Weight factors

µ

Specific growth rate (h-1)

Cross-sectional area of fermenter (m3)

Ci

Concentration of i-component

F

Glucose feed flow rate

Total volumetric mass transfer coefficient (h-1)

Ke

Saturation constant for ethanol

Ki

Inhibition constant

Ko

Saturation constant for dissolved oxygen

Ks

Saturation constant for glucose

Qi

Specific consumption or production rate

Qm

Glucose consumption rate for maintenance energy

So

Glucose concentration of feed

t

Time (hour)

Time delay (hour)

Final time (hour)

V(t)

Cultural volume (m3)

Vfer

Volume of fermentator (m3)

Yield of component i on j

Superscripts and subscripts

*

Interface

c

Carbon dioxide

cr

Critic

e

Ethanol (by-product)

lim

Limitation

max

Maximum

o

Dissolved oxygen

ox

Oxidative

pr

Production

red

Reductive

s

Glucose (substrate)

up

Uptake

x

Yeast (biomass)

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